Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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IMPROVING THE ORDER AND RATES OF CONVERGENCE FOR THE SUPER-HALLEY METHOD IN BANACH SPACES

  • Published : 1998.06.01

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Abstract

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

Keywords

References

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